In a digital transmission system a transmitted signal is constrained to one of a set of possible states. These states might be distinguished by differences in pulse amplitude, position, or width, or by differences in amplitude, phase or frequency of a carrier, or by combination of some of these. What all these methods have in common is the use of a set of distinct transmit stages. The receiver of the system in order to decode the signal, has to recognise each received state correctly. This is made more difficult by a combination of attentuation along the transmission path and noise added to the signal. The noise is generated from a variaety of potential sources, e.g. thermal noise or crosstalk noise from other transmission systems. This perturbs the perceived value of the received signal from its ideal value. The receiver thus has to decide which of the allowed set of transmitted states was most likely to have been sent. If the perturbation is large enough the wrong decision is made and an error or errors are then incorporated in the receiver's digital output(s).
In any transmission system the transmitted signal is modified by the characteristics of the transmission channel as it propagates through it. When the information content of the signal is in digital form, channel impairments will appear as inter-symbol interference (ISI). That is, the energy transmitted in any one baud period is no longer confined to that period when received, but has become smeared over several periods. Modest levels of ISI may only reduce the noise margin of the received bauds whilst larger levels can make the signal completely unreadable without equalization. Perfect equalization consists of passing the received signal through a network whose transfer function is the inverse of the channel's. Perfection, however, is neither attempted nor is it desirable. What is attempted is to reduce the value of ISI at the decision point to zero at the sampling instants.